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Geometry - Polygons

In geometry a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

The word "polygon" derives from the Greek πολύς ("many") and γωνία (gōnia), meaning "knee" or "angle". Today a polygon is more usually understood in terms of sides. - Wikipedia

    K = area
    r= radius of inscribed circle
    R = radius of circumscribed circle
    p and q are diagonals
    n= number of sides
    θ = one of the vertex angles

Right TriangleRight triangle - RF Cafe


 (Pythagorean)






Equilateral Triangle

Equilateral triangle - RF Cafe



Rectangle

Rectangle - RF Cafe
Parallelogram

Parallelogram - RF Cafe





General Quadrilateral

General quadrilateral - RF Cafe

   
  (Bretschneider's Formula)

Cyclic-Inscriptable Quadrilateral

Cyclic inscriptable quadrilateral - RF Cafe





General Triangle

General triangle - RF Cafe
hc = length of altitude on side c,
tc = length of bisector of angle C,
mc = length of median to side c.




(Law of Cosines)


(Heron’s formula)







Rhombus

Rhombus - RF Cafe
Trapezoid

Trapezoid - RF Cafe
 
Regular Polygon

Regular polygon - RF Cafe



   
  
 
Cyclic Quadrilateral

Cyclic quadrilateral - RF Cafe
   (Brahmagupta’s formula)



 


Source: CRC Standard Math Tables, 1987

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